Fundamental Reasoning Paradigms Induce Out-of-Domain Generalization in Language Models

Deduction, induction, and abduction are fundamental reasoning paradigms, core for human logical thinking. Although improving Large Language Model (LLM) reasoning has attracted significant research efforts, the extent to which the fundamental paradigms induce generalization has yet to be systematically explored. In this study, we shed light on how the interplay between these core paradigms influences LLMs' reasoning behavior. To this end, we first collect a new dataset of reasoning trajectories from symbolic tasks, each targeting one of the three fundamental paradigms, to abstract from concrete world knowledge. Then, we investigate effective ways for inducing these skills into LLMs. We experiment with a battery of methods including simple fine-tuning, and more complex approaches to increase model depth, or transform a dense model to a mixture-of-experts. We comprehensively evaluate induced models on realistic out-of-domain tasks, that are entirely formulated in natural language and contain real-world knowledge. Our results reveal that our approach yields strong generalizability with substantial performance gains (up to $14.60$) across realistic tasks.

Progressive Depth Up-scaling via Optimal Transport

Scaling Large Language Models (LLMs) yields performance gains but incurs substantial training costs. Depth up-scaling offers training efficiency by adding new layers to pre-trained models. However, most existing methods copy or average weights from base layers, neglecting neuron permutation differences. This limitation can potentially cause misalignment that harms performance. Inspired by applying Optimal Transport (OT) for neuron alignment, we propose Optimal Transport Depth Up-Scaling (OpT-DeUS). OpT-DeUS aligns and fuses Transformer blocks in adjacent base layers via OT for new layer creation, to mitigate neuron permutation mismatch between layers. OpT-DeUS achieves better overall performance and offers improved training efficiency than existing methods for continual pre-training and supervised fine-tuning across different model sizes. To further evaluate the impact of interpolation positions, our extensive analysis shows that inserting new layers closer to the top results in higher training efficiency due to shorter back-propagation time while obtaining additional performance gains.